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Asymptotic Sharpness of Bounds on Hypertrees

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Lin Y., Kang L., Shan E.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

789-795

The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most [...] (nk−1) $\left( {\matrix{n \cr {k - 1} } } \right)$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.

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1 Discussiones Mathematicae Graph Theory

1 Kang L.

1 Lin Y.

1 Shan E.

1 2017

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Asymptotic Sharpness of Bounds on Hypertrees